17,391 research outputs found
Chebyshev and Conjugate Gradient Filters for Graph Image Denoising
In 3D image/video acquisition, different views are often captured with
varying noise levels across the views. In this paper, we propose a graph-based
image enhancement technique that uses a higher quality view to enhance a
degraded view. A depth map is utilized as auxiliary information to match the
perspectives of the two views. Our method performs graph-based filtering of the
noisy image by directly computing a projection of the image to be filtered onto
a lower dimensional Krylov subspace of the graph Laplacian. We discuss two
graph spectral denoising methods: first using Chebyshev polynomials, and second
using iterations of the conjugate gradient algorithm. Our framework generalizes
previously known polynomial graph filters, and we demonstrate through numerical
simulations that our proposed technique produces subjectively cleaner images
with about 1-3 dB improvement in PSNR over existing polynomial graph filters.Comment: 6 pages, 6 figures, accepted to 2014 IEEE International Conference on
Multimedia and Expo Workshops (ICMEW
Sparse Approximation of 3D Meshes using the Spectral Geometry of the Hamiltonian Operator
The discrete Laplace operator is ubiquitous in spectral shape analysis, since
its eigenfunctions are provably optimal in representing smooth functions
defined on the surface of the shape. Indeed, subspaces defined by its
eigenfunctions have been utilized for shape compression, treating the
coordinates as smooth functions defined on the given surface. However, surfaces
of shapes in nature often contain geometric structures for which the general
smoothness assumption may fail to hold. At the other end, some explicit mesh
compression algorithms utilize the order by which vertices that represent the
surface are traversed, a property which has been ignored in spectral
approaches. Here, we incorporate the order of vertices into an operator that
defines a novel spectral domain. We propose a method for representing 3D meshes
using the spectral geometry of the Hamiltonian operator, integrated within a
sparse approximation framework. We adapt the concept of a potential function
from quantum physics and incorporate vertex ordering information into the
potential, yielding a novel data-dependent operator. The potential function
modifies the spectral geometry of the Laplacian to focus on regions with finer
details of the given surface. By sparsely encoding the geometry of the shape
using the proposed data-dependent basis, we improve compression performance
compared to previous results that use the standard Laplacian basis and spectral
graph wavelets
Random Walk Graph Laplacian based Smoothness Prior for Soft Decoding of JPEG Images
Given the prevalence of JPEG compressed images, optimizing image
reconstruction from the compressed format remains an important problem. Instead
of simply reconstructing a pixel block from the centers of indexed DCT
coefficient quantization bins (hard decoding), soft decoding reconstructs a
block by selecting appropriate coefficient values within the indexed bins with
the help of signal priors. The challenge thus lies in how to define suitable
priors and apply them effectively.
In this paper, we combine three image priors---Laplacian prior for DCT
coefficients, sparsity prior and graph-signal smoothness prior for image
patches---to construct an efficient JPEG soft decoding algorithm. Specifically,
we first use the Laplacian prior to compute a minimum mean square error (MMSE)
initial solution for each code block. Next, we show that while the sparsity
prior can reduce block artifacts, limiting the size of the over-complete
dictionary (to lower computation) would lead to poor recovery of high DCT
frequencies. To alleviate this problem, we design a new graph-signal smoothness
prior (desired signal has mainly low graph frequencies) based on the left
eigenvectors of the random walk graph Laplacian matrix (LERaG). Compared to
previous graph-signal smoothness priors, LERaG has desirable image filtering
properties with low computation overhead. We demonstrate how LERaG can
facilitate recovery of high DCT frequencies of a piecewise smooth (PWS) signal
via an interpretation of low graph frequency components as relaxed solutions to
normalized cut in spectral clustering. Finally, we construct a soft decoding
algorithm using the three signal priors with appropriate prior weights.
Experimental results show that our proposal outperforms state-of-the-art soft
decoding algorithms in both objective and subjective evaluations noticeably
Hypergraph p-Laplacian Regularization for Remote Sensing Image Recognition
It is of great importance to preserve locality and similarity information in
semi-supervised learning (SSL) based applications. Graph based SSL and manifold
regularization based SSL including Laplacian regularization (LapR) and
Hypergraph Laplacian regularization (HLapR) are representative SSL methods and
have achieved prominent performance by exploiting the relationship of sample
distribution. However, it is still a great challenge to exactly explore and
exploit the local structure of the data distribution. In this paper, we present
an effect and effective approximation algorithm of Hypergraph p-Laplacian and
then propose Hypergraph p-Laplacian regularization (HpLapR) to preserve the
geometry of the probability distribution. In particular, p-Laplacian is a
nonlinear generalization of the standard graph Laplacian and Hypergraph is a
generalization of a standard graph. Therefore, the proposed HpLapR provides
more potential to exploiting the local structure preserving. We apply HpLapR to
logistic regression and conduct the implementations for remote sensing image
recognition. We compare the proposed HpLapR to several popular manifold
regularization based SSL methods including LapR, HLapR and HpLapR on UC-Merced
dataset. The experimental results demonstrate the superiority of the proposed
HpLapR.Comment: 9 pages, 6 figure
Cross-label Suppression: A Discriminative and Fast Dictionary Learning with Group Regularization
This paper addresses image classification through learning a compact and
discriminative dictionary efficiently. Given a structured dictionary with each
atom (columns in the dictionary matrix) related to some label, we propose
cross-label suppression constraint to enlarge the difference among
representations for different classes. Meanwhile, we introduce group
regularization to enforce representations to preserve label properties of
original samples, meaning the representations for the same class are encouraged
to be similar. Upon the cross-label suppression, we don't resort to
frequently-used -norm or -norm for coding, and obtain
computational efficiency without losing the discriminative power for
categorization. Moreover, two simple classification schemes are also developed
to take full advantage of the learnt dictionary. Extensive experiments on six
data sets including face recognition, object categorization, scene
classification, texture recognition and sport action categorization are
conducted, and the results show that the proposed approach can outperform lots
of recently presented dictionary algorithms on both recognition accuracy and
computational efficiency.Comment: 36 pages, 12 figures, 11 table
A Survey on Learning to Hash
Nearest neighbor search is a problem of finding the data points from the
database such that the distances from them to the query point are the smallest.
Learning to hash is one of the major solutions to this problem and has been
widely studied recently. In this paper, we present a comprehensive survey of
the learning to hash algorithms, categorize them according to the manners of
preserving the similarities into: pairwise similarity preserving, multiwise
similarity preserving, implicit similarity preserving, as well as quantization,
and discuss their relations. We separate quantization from pairwise similarity
preserving as the objective function is very different though quantization, as
we show, can be derived from preserving the pairwise similarities. In addition,
we present the evaluation protocols, and the general performance analysis, and
point out that the quantization algorithms perform superiorly in terms of
search accuracy, search time cost, and space cost. Finally, we introduce a few
emerging topics.Comment: To appear in IEEE Transactions On Pattern Analysis and Machine
Intelligence (TPAMI
Graph Regularized Low Rank Representation for Aerosol Optical Depth Retrieval
In this paper, we propose a novel data-driven regression model for aerosol
optical depth (AOD) retrieval. First, we adopt a low rank representation (LRR)
model to learn a powerful representation of the spectral response. Then, graph
regularization is incorporated into the LRR model to capture the local
structure information and the nonlinear property of the remote-sensing data.
Since it is easy to acquire the rich satellite-retrieval results, we use them
as a baseline to construct the graph. Finally, the learned feature
representation is feeded into support vector machine (SVM) to retrieve AOD.
Experiments are conducted on two widely used data sets acquired by different
sensors, and the experimental results show that the proposed method can achieve
superior performance compared to the physical models and other state-of-the-art
empirical models.Comment: 16 pages, 6 figure
Learning parametric dictionaries for graph signals
In sparse signal representation, the choice of a dictionary often involves a
tradeoff between two desirable properties -- the ability to adapt to specific
signal data and a fast implementation of the dictionary. To sparsely represent
signals residing on weighted graphs, an additional design challenge is to
incorporate the intrinsic geometric structure of the irregular data domain into
the atoms of the dictionary. In this work, we propose a parametric dictionary
learning algorithm to design data-adapted, structured dictionaries that
sparsely represent graph signals. In particular, we model graph signals as
combinations of overlapping local patterns. We impose the constraint that each
dictionary is a concatenation of subdictionaries, with each subdictionary being
a polynomial of the graph Laplacian matrix, representing a single pattern
translated to different areas of the graph. The learning algorithm adapts the
patterns to a training set of graph signals. Experimental results on both
synthetic and real datasets demonstrate that the dictionaries learned by the
proposed algorithm are competitive with and often better than unstructured
dictionaries learned by state-of-the-art numerical learning algorithms in terms
of sparse approximation of graph signals. In contrast to the unstructured
dictionaries, however, the dictionaries learned by the proposed algorithm
feature localized atoms and can be implemented in a computationally efficient
manner in signal processing tasks such as compression, denoising, and
classification
Sketch-based subspace clustering of hyperspectral images
Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images
HVS-Based Perceptual Color Compression of Image Data
In perceptual image coding applications, the main objective is to decrease,
as much as possible, Bits Per Pixel (BPP) while avoiding noticeable distortions
in the reconstructed image. In this paper, we propose a novel perceptual image
coding technique, named Perceptual Color Compression (PCC). PCC is based on a
novel model related to Human Visual System (HVS) spectral sensitivity and
CIELAB Just Noticeable Color Difference (JNCD). We utilize this modeling to
capitalize on the inability of the HVS to perceptually differentiate photons in
very similar wavelength bands (e.g., distinguishing very similar shades of a
particular color or different colors that look similar). The proposed PCC
technique can be used with RGB (4:4:4) image data of various bit depths and
spatial resolutions. In the evaluations, we compare the proposed PCC technique
with a set of reference methods including Versatile Video Coding (VVC) and High
Efficiency Video Coding (HEVC) in addition to two other recently proposed
algorithms. Our PCC method attains considerable BPP reductions compared with
all four reference techniques including, on average, 52.6% BPP reductions
compared with VVC (VVC in All Intra still image coding mode). Regarding image
perceptual reconstruction quality, PCC achieves a score of SSIM = 0.99 in all
tests in addition to a score of MS-SSIM = 0.99 in all but one test. Moreover,
MOS = 5 is attained in 75% of subjective evaluation assessments conducted.Comment: Preprint: 2021 IEEE International Conference on Acoustics, Speech and
Signal Processing (ICASSP 2021
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